How to Network with nurse recruiters?

I am doing a new grad residency program that is not paid and does not guarantee a job at the end, although they do offer job placement assistance ( the program starts in next month) and I recently spoke to a nurse recruiter from a different hospital, I told her about me being in this program and she said to keep in touch and that she was really interested in me.

I want to make sure I stay in her radar but I don't know what to email her about (the residency is 4mo long). I guess what I am asking is If any one has any ideas on things I could bring up or email her about to make sure my name stays fresh in her head and she'll want to help me get a job? Also how often should I network with her until my residency is over?

I have no other job leads (no interviews since I graduated) besides her and I am really hopeful this will work out for me even tho I feel like 4 months is a long time to wait. This place would be my #1 choice so I am willing to bide my time if in the end I am able to get what I want. I don't have much experience in networking...Please help........